Lenells, J.; Fokas, A. S. On a novel integrable generalization of the nonlinear Schrödinger equation. (English) Zbl 1160.35536 Nonlinearity 22, No. 1, 11-27 (2009). Summary: We consider an integrable generalization of the nonlinear Schrödinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS equation in the same way as the Camassa-Holm equation is related to the KdV equation. In this paper we (a) use the bi-Hamiltonian structure to write down the first few conservation laws, (b) derive a Lax pair, (c) use the Lax pair to solve the initial value problem and (d) analyse solitons. Cited in 2 ReviewsCited in 58 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) Keywords:nonlinear Schrödinger equation; Cauchy problem; bi-Hamiltonian structure; conservation laws; Lax pair; solitons PDFBibTeX XMLCite \textit{J. Lenells} and \textit{A. S. Fokas}, Nonlinearity 22, No. 1, 11--27 (2009; Zbl 1160.35536) Full Text: DOI arXiv